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Math Help - Curve Sketching

  1. #1
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    Curve Sketching

    Show that for any cubic function of the form y = ax3 + bx2 + cx + d, there is a single point of inflection where the slope of the curve at that point is C b2 / 3a.
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    I would suggest making \frac{dy}{dx} =
    Quote Originally Posted by steezin View Post
    C b2 / 3a.
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  3. #3
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    Quote Originally Posted by steezin View Post
    Show that for any cubic function of the form y = ax3 + bx2 + cx + d, there is a single point of inflection where the slope of the curve at that point is C b2 / 3a.
    It follows from the definition that the x-coord of the point of inflection occurs where dy/dx has a turning point.
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  4. #4
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    Quote Originally Posted by steezin View Post
    Show that for any cubic function of the form y = ax3 + bx2 + cx + d, there is a single point of inflection where the slope of the curve at that point is C b2 / 3a.
    Sounds straightforward to me. An inflection point occurs where the second derivative is 0. Set the second derivative equal to 0 and solve for x. Then calculate the first derivative for that x.
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